The book is meant for undergraduates in the life sciences who only have one semester of calculus as background. It is therefore appropriate that the book starts with a very long and gentle introduction. Systems of linear differential equations are not discussed until chapter five.

The style and concept of the book is markedly different from the usual textbooks on differential equations that are written for an engineering audience. The chapters are shorter, new material is introduced at a slower pace, and there are very few textbook-like examples focusing on theoretical aspects. There are almost no proofs. There are, on the other hand, real-life examples and actual research papers in each chapter.

The most significant difference, however, is that there are very few exercises (probably less than five per chapter). This reviewer thinks that students learning from this book will be able to understand research papers using the notions explained here if they do not differ from the examples covered in this book by too much, but that is how far their knowledge will go. They will not be able to apply their knowledge in different circumstances because they will simply not have enough practice in using these concepts, methods and notions on their own.

The back cover of the book says that the book is based on a very successful one-semester course at Harvard University. This reviewer does not doubt that there could be specific circumstances in which this textbook is the right choice, so if you think yours might be one of those circumstances, certainly take a look at this book. From time to time, however, you will need to check that your students can apply these techniques, not just understand when others use them.

Miklós Bóna is Associate Professor of Mathematics at the University of Florida.